413400 has 96 divisors (see below), whose sum is σ = 1406160. Its totient is φ = 99840.

The previous prime is 413353. The next prime is 413411. The reversal of 413400 is 4314.

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 7774 + ... + 7826.

2⁴¹³⁴⁰⁰ is an apocalyptic number.

413400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (703080).

413400 is an abundant number, since it is smaller than the sum of its proper divisors (992760).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

413400 is a wasteful number, since it uses less digits than its factorization.

413400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 85 (or 76 counting only the distinct ones).

The product of its (nonzero) digits is 48, while the sum is 12.

The square root of 413400 is about 642.9618962271. The cubic root of 413400 is about 74.4943767057.

Adding to 413400 its reverse (4314), we get a palindrome (417714).

The spelling of 413400 in words is "four hundred thirteen thousand, four hundred".